Add electron/positron Single (Coulomb) Scattering Model

[whokion]

The single elastic scattering is an alternative to the multiple scattering process when the average number of collisions per charged track is relatively small or in low-density gaseous media. It can be also used in mixed simulation algorithms to describe charged particle transport more accurately in physical content, but still in a computationally efficient way. We implement an electron/positron Coulomb Scattering model of Wenzel [ref: G. Wentzel, Z. Phys. 40 (1927) 590] based on G4CoulombScattering process and G4eCoulombScatteringModel. For details, refer to the section, 8.2 of the Geant4 physics manual, Release 10.7 or
the paper by J.M. Fernández-Varea, R. Mayol, J. Baró and F. Salvat, On the theory and simulation of multiple elastic scattering of electrons. Nucl. Instrum. and Meth. in Phys. Research B, 73 (1993) 447–473, doi:10.1016/0168-583X(93)95827-R. The following is a list of related sub-tasks:

• [ ] Add nuclear_mass in ElementRecord equivalent to G4NucleiProperties::GetNuclearMass and an associated accessor in MaterialParams, and a unit test
  • Need for refactoring G4eCoulombScatteringModel::SampleSecondaries and G4ScreeningMottCrossSection::SetupKinematic (and other hadronic models)
  • Import it from Geant4 (GeantImport)
  • Need an approximation to use the average atomic mass (i.e, not using Isotopes of an element) instead of G4VEmModel::SelectIsotopeNumber
• [ ] Implement helpers equivalent to G4WentzelOKandVIxSection and G4ScreeningMottCrossSections, and a unit test
• [ ] Implement CoulombScatteringData necessary for G4eCoulombScatteringModel
• [ ] Implement CoulombScatteringProcess, CoulombScatteringModel and CoulombScatteringInteractor based on G4eCoulombScatteringModel and G4CoulombScattering, and unit tests
• [ ] Integrate codes into the celeritas simulation pipeline (celer-sim and celer-g4 applications)

[sethrj]

For G4NucleiProperties I think we should extend the MaterialParams to have nuclides as well as elements; the nuclide data would include binding energies imported from Geant4 via GeantImporter and associated classes.

[whokion]

That would be great as G4NucleiProperties will be used in many other places (in hadronic physics models including photo- and eletro-nuclear interactions). So, should we open another issue for extending MaterialParams to cover G4NucleiProperties and related classes?

[sethrj]

I think that the Nuclide upgrade would make a good first pull request: it's small enough and self contained. Then after that, based on a quick review of the Geant4 classes, I'd refactor the G4WentzelOKandVIxSection, G4eCoulombScatteringModel, and G4CoulombScattering into several classes:

• [ ] CoulombScatteringData and a corresponding Model class to manage the data
• [ ] CoulombScatteringView which would take a material and energy and have the helper functions like calc_nuclear_xs, calc_electron_xs
• [x] I don't think it need to calculate cross sections on the fly , but if it does make a CoulombScatteringXsCalculator forG4eCoulombScatteringModel::ComputeCrossSectionPerAtom
• [ ] G4WentzelOKandVIxSection::SampleSingleScattering becomes a Distribution that samples polar angle
• [ ] G4eCoulombScatteringModel::SampleSecondaries becomes an Interactor
• [ ] Create the Process and add the interfaces to move the data from GeantImporter

And since a lot of these are tied to the WentzelOKandVI model which is abbreviated wokvi maybe some of these classes should have a Wokvi or WOI prefix instead of CoulombScattering?

[whokion]

Yes, we do not need to implement G4eCoulombScatteringModel::ComputeCrossSectionPerAtom as the lambda table for the CoulombScattering process will be imported from Geant4 (and do not need G4WentzelOKandVIxSection::ComputeTransportCrossSectionPerAtom either), but excerpt only relevant parts of G4WentzelOKandVIxSection that need for an Interactor associated with the model. So, can @stognini help for extending MaterialParams while Hayden reviews other relevant classes and start to implement them as parallel?

[hhollenb]

Add G4ScreeningMottCrossSections

[sethrj]

Starting point for material data:

//---------------------------------------------------------------------------//
/*!
 * Fundamental, invariant properties of a nuclide.
 */
struct NuclideRecord
{
    AtomicNumber atomic_number;  //!< Z number
    AtomicNumber atomic_mass;  //!< A number (TODO: fix type?)
    units::AmuMass atomic_mass;  //!< Isotope-weighted average atomic mass
};

//---------------------------------------------------------------------------//
/*!
 * Fractional element component of a material.
 *
 * This represents, e.g., the fraction of hydrogen in water.
 */
struct ElNuclideComponent
{
    NuclideId nuclide;  //!< Index in MaterialParams elements
    real_type fraction;  //!< Fraction of number density
};

//---------------------------------------------------------------------------//
/*!
 * Fundamental, invariant properties of an element.
 *
 * Add elemental properties as needed if they apply to more than one physics
 * model. (When nuclear physics is implemented, add isotopes.)
 *
 * Note that more than one "element def" can exist for a single atomic number:
 * there might be different enrichments of an element in the problem.
 */
struct ElementRecord
{
    AtomicNumber atomic_number;  //!< Z number
    units::AmuMass atomic_mass;  //!< Isotope-weighted average atomic mass
    ItemRange<ElNuclideComponent> nuclides;  //!< Nuclide components

[sethrj]

Completed by #861 and #899